LIMITING ERROR OF THE OPTIMAL COMPUTING UNIT FOR FUNCTIONS FROM THE CLASS (Formula Presented)
Utessov A.B. Utessova G.I.
30 September 2025al-Farabi Kazakh State National University
KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2025#127Issue 3106 - 116 pp.
In the problem of optimal recovery of an infinite object (functions on a continuum, integrals of continuous functions, solutions of partial differential equations, derivative of functions,…) from finite numerical information about it, the problem of finding the limiting error of the optimal computing unit naturally arises, since the numerical information about the infinite object to be restored, as a rule, will not be accurate. In this article, the limiting error of the optimal computing unit is found in the problem of optimal recovery of periodic functions of many variables from the anisotropic Sobolev class (Formula Presented) in a power-logarithmic scale in the space metric L2. The actuality of this work is determined by the following factors: firstly, the found limiting error εN of the optimal computing unit preserves the exact order of the smallest recovery error, when replacing exact numerical information about a function (Formula Presented) with inaccurate information and is unimprovable in order; secondly, the problem of finding the limiting error of an optimal computing unit has not previously been studied in the class under consideration; thirdly, the anisotropic Sobolev class in the power-logarithmic scale is a finer scale of classification of periodic functions according to the rate of decrease of their trigonometric Fourier coefficients than the anisotropic Sobolev class in the power scale.
anisotropic Sobolev class , exact order , limiting error , linear functionals , optimal computing unit , optimal recovery , trigonometric Fourier coefficients
Text of the article Перейти на текст статьи
Department Mathematics, Aktobe regional university named after K. Zhubanov, Aktobe, Kazakhstan
Department Computer Science and Information Technologies, Aktobe regional university named after K. Zhubanov, Aktobe, Kazakhstan
Department Mathematics
Department Computer Science and Information Technologies
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026